Welcome!
The Canon 50mm f/1.8 is definitely a very good place to start your lens collection. Cheap and sharp optics, if not the best build quality.
You said that the kit lens "just doesn't hold up to the quality of images I've seen other lenses get out of the T2i," which does have a fair bit of truth in it, and while the glass in a setup does have a massive effect on quality, it also comes down to what you're shooting and the skill of the operator. Roger Deakins or David Mullen could eke far more exquisite images out of a 550D and the kit lens then I could with a set of Zeiss Compact Primes.
Remember that you'll also probably be looking at images that have had hours spent on them a post - while the mantra "garbage in, garbage out" is still as true as ever, even a not-so-good colour grader (like me) can make a decent image shine. I posted this
Kilver Court Gardens in another thread the other day, and it's a great example of what the kit lens can do with well-composed shots, a little bit of colour correction and nice natural light.
All of that said… you will want to use more than just the kit lens. It is a very nice little lens, with a good focal range on the 550D, but if you're not shooting in a daylight exterior or brightly lit room it's often not fast enough. If you're not familiar with the term "speed" when talking about lenses (I'm sorry if you are, but someone else might find it useful), it refers to how much light a lens lets in - the faster the lens, the more light. Two figures are given when talking about lenses - the focal length (in mm) and the f-stop. The larger the focal length, the more "zoomed-in" the lens is, and the smaller the f-stop the faster it is.
Now we've got that out the way, let's move on to primes v zooms. Basically, primes are usually faster than zooms that can do the same focal length, cheaper than zoom lenses of the same f-stop, and generally have sharper optics as they don't need as many glass elements. BUT - they don't offer you the same flexibility as a zoom lens does when shooting things that are unscripted or just a little more loose in style. If you're planning to do documentary work or improvisational drama then zooms may be a better choice, but when doing conventional drama and music videos, the time it takes to change a lens doesn't really delay things.
If you want fast lenses but don't want to spend a lot of money, go for primes. If you want more flexibility and aren't bothered about speed, get a zoom or two. If you want flexibility and fast lenses, empty your wallet and get a mixture!
Finally, I've gone (for the time being) the very cheap route, and am buying some gorgeous vintage primes off eBay for a fraction of the price of their modern equivalents. I love the look of them (though it isn't for everyone), but they do have their downsides, mainly no aperture (f-stop) control from the camera (you have to use a ring on the lens), and no autofocus for stills photography, but I think it's worth the sacrifice for the cost and look of them.
I've rambled on for far too long - best of luck!